Given an input point cloud denoted as \(P \in \mathbb {R}^{3\times N}\) , a set of nodes \(\mathfrak {P}^{(1)}\in \mathbb {R}^{3\times M_1}\)  is sampled by Farthest Point Sampling (FPS). A point-to-node grouping [1]} is performed to obtain \(M_1\)  clusters of points. Each cluster is processed by a PointNet [2]} to get \(M_1\)  feature vectors of length \(C_1\) , respectively, i.e. \(P^{(1)}\in \mathbb {R}^{C_1\times M_1}\) . The point-to-node grouping is adaptive to the density of points. This is beneficial especially for point clouds from Lidar scans, where points are sparse at far range and dense at near range. The above sampling-grouping-PointNet operation is performed again to obtain another set of feature vectors \(P^{(2)} \in \mathbb {R}^{C_2\times M_2}\) . Finally, a PointNet is applied to obtain the global point cloud feature vector \(P^{(3)}\in \mathbb {R}^{C_3\times 1}\) .
